The mole fraction at equilibrium is calculated by dividing the number of moles of a specific gas by the total number of moles of all gases present at equilibrium.
Understanding Mole Fraction
Mole fraction (often denoted as xA for component A) represents the ratio of the number of moles of a particular component in a mixture to the total number of moles of all components in the mixture. At equilibrium, this ratio remains constant.
Steps to Calculate Mole Fraction at Equilibrium
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Determine the Equilibrium Moles of Each Gas: This is often the most challenging part. You might need to use an ICE (Initial, Change, Equilibrium) table in conjunction with the equilibrium constant (K) to find the number of moles of each gas at equilibrium.
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Calculate the Total Number of Moles: Sum the number of moles of each gas present at equilibrium.
Total moles = moles A + moles B + moles C + ... -
Calculate the Mole Fraction of Each Gas: Divide the number of moles of each gas at equilibrium by the total number of moles.
- xA = (moles of A) / (total moles)
- xB = (moles of B) / (total moles)
- xC = (moles of C) / (total moles)
- And so on...
Example
Consider the reversible reaction:
N2(g) + 3H2(g) ⇌ 2NH3(g)
At equilibrium, let's say we have:
- Moles of N2 = 1 mole
- Moles of H2 = 3 moles
- Moles of NH3 = 2 moles
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Total moles: 1 + 3 + 2 = 6 moles
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Mole fractions:
- xN2 = 1/6 = 0.167
- xH2 = 3/6 = 0.5
- xNH3 = 2/6 = 0.333
Note that the sum of all mole fractions should equal 1 (0.167 + 0.5 + 0.333 ≈ 1).
Importance of Mole Fraction
- Partial Pressure Calculations: Mole fraction is used to calculate the partial pressure of a gas in a mixture using Dalton's Law of Partial Pressures: PA = xA * Ptotal, where PA is the partial pressure of gas A, xA is its mole fraction, and Ptotal is the total pressure.
- Thermodynamics: Mole fraction is a key component in many thermodynamic calculations, such as determining the activity of a component in a mixture.
